• Support PF! Buy your school textbooks, materials and every day products Here!

Determining Coplanarity of four points

  • Thread starter jrotmensen
  • Start date
  • #1
How do you determine Coplanarity of four points?
I am given A(3,1,0), B(2,-3,1), C(-1,0,4), D(5,-6,-2).

Do i make vectors for each point from the origin? (But that wouldn't work would it? :()
Can anybody point me in the right direction?

Thanks!
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
if a,b,c are coplanar vectors then
a.(bxc)=0
 
  • #3
if a,b,c are coplanar vectors then
a.(bxc)=0
at this point, we havent learned vector*vector multiplication.
is there any other way?

also, how should i get the vectors??? displacement of the point from the origin? or displacement from one point to another??
 
Last edited:
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,777
911
The equation of any plane (that does not include the origin) can be written in the form Ax+ By+ Cz= 1. Replace x, y, and z by the coordinates of three of your points to get three equations to solve for A, B, and C. (If you can't, it is because the plane includes the origin- so try again with Ax+ By+ Cz= 0.)

Once you have the equation of the plane that contains three of the points, put the coordinates of the fourth point into that equation and see if they also satify the equation.
 

Related Threads for: Determining Coplanarity of four points

  • Last Post
2
Replies
49
Views
4K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
4
Views
28K
  • Last Post
Replies
2
Views
8K
  • Last Post
Replies
15
Views
4K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
3K
Replies
5
Views
12K
Top